A perfect mirror means, that all the photons which collided with the mirror will be reflected in the same amount, with the same energy and with the same - except sign - angle. Will the mirror get an impulse from the photons?
Yes it will.
Assuming the light is incedent normally the change in the photon momentum is $2h\nu/c$, and consequently the momentum of the mirror will change by the same amount.
If the mirror is free to move it will be accelerated by the light and as a result the light will be slightly red shifted. There is more discussion of this in Can relativistic momentum (photons) be used as propulsion for 'free' after the initial generation? though the question is not an exact duplicate.
@HolgerFieldler @John Rennie ....Just for good measure and interest I would like to proffer a Maxwellian interpretation of mirrors. A practical mirror, say, aluminum or silver, will feel the repulsive force of Lenz's law. A simple explanation follows: The magnetic component of the impinging plane wave accelerates electron's in the silver, the subsequent magnetic field vector is parallel to the incident magnetic vector, and as we all know like poles repel, vectors in this case. This is Lenz's law. The impedance of free space is 377 Ohms the impedance of the silver will be in the order of Ohms, such a mismatch generates maximum reflection and repulsion, a blackened surface will represent a higher impedance and less reflection, therefore less repulsion. It is interesting to contemplate whether a 377 Ohm piece of "space paper" (often used by microwave engineer's) would reduce the repulsion to zero? No reflection. The E vector attraction cancels the B vector repulsion? Further contemplation suggests for high impedance surfaces (say, above 377 Ohm's, a dielectric material) attraction may occur?